Search

In view of the current null results for the popular models of physics beyond the standard model, it has become necessary to explore other plausible alternatives for such physics.Non-commutative spaces, which can arise in specific string theory models, is one such alternative. We explore the possibility that quarks and leptons exist in such spaces, and obtain a bound on the scale of non-commutativity.

Lattice techniques are the most reliable ones to investigate the QCD phase diagram in the temperature-baryon density (chemical potential) plane. These techniques are, however, well-known to be saddled with a variety of problems at nonzero density. I address here the old question of placing the baryonic (quark) chemical potential on the lattice and point out its important consequences for the current and future experimental searches of the QCD critical point., Comment: 8 pages, 3 figures, talk presented at the 38th International Symposium on Lattice Field Theory - LATTICE2021, 26th-30th, July, 2021, Zoom/Gather@Massachusetts Institute of Technology

Extending the successes of lattice quantum chromodynamics(QCD) at zero as well as nonzero temperatures to nonzero density is extremely desirable in view of the quest for the QCD phase diagram both theoretically and experimentally. It turns out though to give rise to some conundrums whose resolution may assist progress in this exciting but difficult area, and should therefore be sought actively., Comment: 11 pages, 6 figures, To appear in the proceeding of the international conference on "Criticality in QCD and the Hadron Resonance Gas", 29-31 July 2020, Wroclaw, Poland

One of the main goals of the cold baryonic matter (CBM) experiment at FAIR is to explore the phases of strongly interacting matter at finite temperature and baryon chemical potential μ B . The equation of state of quantum chromodynamics (QCD) at μ B > 0 is an essential input for the CBM experiment, as well as for the beam energy scan in the Relativistic Heavy Ion Collider(RHIC) experiment. Unfortunately, it is highly nontrivial to calculate the equation of state directly from QCD: numerical Monte Carlo studies on lattice are not useful at finite μ B . Using the method of Taylor expansion in chemical potential, we estimate the equation of state, namely the baryon number density and its contribution to the pressure, for two-flavor QCD at moderate μ B . We also study the quark number susceptibilities. We examine the technicalities associated with summing the Taylor series, and explore a Pade resummation. An examination of the Taylor series can be used to get an estimate of the location of the critical point in μ B , T plane.

Strongly interacting matter, which makes up the nuclei of atoms, is described by a theory called quantum chromodynamics (QCD). A critical point in the phase diagram of QCD, if established either theoretically or experimentally, would be as profound a discovery as the familiar gas–liquid critical point discovered in the nineteenth century. Due to the extremely short-lived nature of the concerned phases, novel experimental techniques are needed to search for it. The Relativistic Heavy Ion Collider (RHIC) in USA has an experimental programme which can fit the bill to do so. Theoretical techniques of Lattice QCD, which is QCD defined on a discrete space-time lattice, have provided glimpses into where the QCD critical point may be, and how to search for it in the experimental data. A brief overview of the theoretical and experimental attempts is provided.

Examining quantum electrodynamics in non-commutative (NC) spaces along with composite operators in these spaces, we show that i) any charge g for a fermion matter field is allowed provided the basic NC photon-photon coupling is g, however no other multiples of g are permitted and ii) composite operators do not have a simple transformation which can be attributed to the effective total charge of the composite particle. Taken together these results place a limit on the scale of non-commutativity to be at most smaller that current LHC limits for compositeness. Furthermore, they also suggest that a substructure at still smaller scales is needed if such spaces are to be a physical reality., 9 pages

The freeze-out curve in the QCD phase diagram embodies a substantial amount of precise experimental data in heavy ion collisions. We present our lattice QCD results along the freeze-out curve. The variance, skew and kurtosis of the event distribution of baryon number are studied at several energies of interest through Pade resummations. A smooth behaviour is predicted for three ratios of these quantities at current RHIC and future LHC energies. Any deviations from these at the RHIC energy scan would signal the presence of a nearby critical point. Our lattice results on the critical point do show such a behaviour.

We present lattice QCD results along the freezeout curve of heavy-ion collisions for the ongoing RHIC energy scan as well as the LHC heavy-ion runs planned for this year. The skew and kurtosis of the event distribution of baryon number are positive at all energies studied, We predict three ratios of non-linear susceptibilities along the freezeout curve as functions of the colliding energy, Sqrt[S_{NN}]. They have smooth behaviour except in the vicinity of a critical point; this can have multiple benefits.

We propose an improvement of the differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method our technique yields positive pressure for all temperatures including in the transition region. Employing it on temporal lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we obtained the pressure, energy density, entropy density, specific heat and speed of sound in quenched QCD for 0.9 < T/Tc < 3. A comparison of our results is made with those from the dimensional reduction approach and a conformal symmetric theory at high-temperature.

We pursue the idea of adding the naive $\mu N$ term, where $\mu$ is the quark chemical potential and $N$ is the conserved quark number, to the lattice QCD action. While computations of higher order susceptibilities, required for estimating the location of the QCD critical point, need a lot fewer number of quark propagators at any order as a result, it has its problem. We discuss a solution, and examine if it works., Comment: Proceedings for the 9th International Workshop on Critical Point and Onset of Deconfinement - CPOD2014, 17-12 November 2014, ZiF, University of Bielefeld, Germany

I review a few selected topics in Lattice Quantum Chromo Dynamics, focusing more on the recent results. These include i) the equation of state and speed of sound, ii) J/\psi suppression, iii) flavour correlations and iv) the QCD phase diagram in the \mu-T plane., Comment: 13 Pages including figures, Plenary Talk at the 9th Workshop on High Energy Physics Phenomenology, ``WHEPP9'', Bhubaneswar, India, January 3-14, 2006, To appear in Pramana

I present our recent results on the critical end point in the \mu_B-T phase diagram of QCD with two flavours of light dynamical quarks and compare them with similar results from other groups. Implications for a possible energy scan at the RHIC are discussed. I also comment briefly on the new results of great relevance to heavy ion collisions from finite temperature lattice QCD simulations on speed of sound, specific heat and on the fate of J/\psi., Comment: Invited Plenary Talk given at 5th International Conference on Physics and Astrophysics of Quark Gluon Plasma, Kolkata, India, February 8-12, 2005; LaTeX in Journal of Physics G style; 9 pages including figures

I review some topics in lattice quantum chromodynamics, focusing more on the recent results. These include: (i) the QCD phase diagram in the μ-T plane, (ii) the quark number susceptibilities, and (iii) the screening lengths.

The deconfinement transition in SU(4) lattice gauge theory is investigated on N_s^3 X N_t lattices for N_s = 8-16 and N_t = 4-8 using a modified Wilson action which is expected to be free of any bulk transitions. The susceptibility chi_{|L|}^{max}, where L is the order parameter for deconfinement, is found to increase linearly with spatial volume for N_t = 4, 5, and 6, indicating a first order deconfinement phase transition. The latent heat of the transition is estimated to be approximately 2/3 of the corresponding ideal gas energy density at T_c., 17 pages. LaTeX, 10 figures

Results from our recent investigations of quark number susceptibilities in both quenched and 2-flavour QCD are presented as a function of valence quark mass and temperature. A strong reduction (approx. 40%) is seen in the strange quark susceptibility above T_c in both the cases. A comparison of our isospin susceptibility results with the corresponding weak coupling expansion reveals once again the non-perturbative nature of the plasma up to 3T_c. Evidence relating the susceptibility to another non-perturbative phenomena, pionic screening lengths, is presented., Talk presented at the 18th Alexander von Humboldt symposium ``100 Years Werner Heisenberg - Works and Impact'', Bamberg, Germany, September 26-30, 2001. 6 pages, LaTeX, buckow.sty needed

We compare the low eigenvalue spectra of the Overlap Dirac operator on two sets of configurations at $\mu_I/\mu_I^c$ = 0.5 and 1.5 generated with dynamical staggered fermions at these isospin chemical potential on $24^3 \times 6$ lattices. We find very small changes in the number of zero modes and low lying modes which is in stark contrast with those across the corresponding finite temperature phases where one sees a drop across the phase transition. Possible consequences are discussed., Comment: 6 Pages, 3 Figures, Submitted for the proceedings of the 10th International Conference on Critical Point and Onset of Deconfinement (CPOD 2016), Wroclaw, Poland

Results from our simulations of QCD with two light dynamical staggered flavours of mass m/Tc=0.1 are presented. Employing our earlier proposed Taylor series method for the baryonic susceptibility, we estimate the radius of convergence by using terms up to the eighth order susceptibility, χ8. Comparing with earlier results on coarser lattices, we find a very good agreement between the Nt =8 and 6 lattices for its location in the ( μB/T ,T/Tc) plane, suggesting any cut-off effects to be encouragingly small.

A critical point in the phase diagram of Quantum Chromodynamics (QCD), if established either theoretically or experimentally, would be as profound a discovery as the good-old gas-liquid critical point. Unlike the latter, however, first-principles based approaches are being employed to locate it theoretically. Due to the short lived nature of the concerned phases, novel experimental techniques are needed to search for it. The Relativistic Heavy Ion Collider (RHIC) in USA has an experimental program to do so. This short review is an attempt to provide a glimpse of the race between the theorists and the experimentalists as well as that of the synergy between them., 15 Pages, Invited Review for Pramana

We report the first measurements of sixth order non-linear quark number susceptibilities in continuum QCD. This extends our earlier computation of the continuum limit of non-linear quark number susceptibilities and the pressure in QCD for m/Tc=0.1. For T/Tc > 1.5, no phase transitions are observable for mu, 3 pages, 4 figures, Lattice2003(nonzero)

Quark number susceptibilities approach their ideal gas limit at sufficiently high temperatures. As in the case of other thermodynamic quantities, this limit itself is altered substantially on lattices with small temporal extent, N_t = 4-8, making it thus difficult to check the validity of perturbation theory. Unlike other observables, improving susceptibilities or number densities is subject to constraints of current conservation and absence of chemical potential dependent divergences. We construct such an improved number density and susceptibility for staggered fermions and show that they approximate the continuum ideal gas limit better on small temporal lattices., Comment: Lattice2002(nonzerot), 3 pages, 3 figures

We calculate the momentum diffusion coefficient for heavy quarks in SU(3) gluon plasma at temperatures 1-2 times the deconfinement temperature. The momentum diffusion coefficient is extracted from a Monte Carlo calculation of the correlation function of color electric fields, in the leading order of expansion in heavy quark mass. Systematics of the calculation are examined, and compared with perturbtion theory and other estimates., 7 pages, 4 figures. Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia

We present results of our simulations of QCD with two light dynamical quarks on a 32^3 X 8 lattice at a current quark mass tuned to have the Goldstone pion mass of about 230 MeV. Employing the Taylor expansion method we proposed earlier, we estimate the radius of convergence of the series for the baryonic susceptibility by using terms up to eighth order. Together with our earlier results, corresponding to the same physical parameters but on coarser lattices at respectively 1.33 times and twice the lattice cut-off (a), we were able to attempt a march towards the continuum limit., Comment: 4 pages, 4 figures, To appear in the proceedings of the 23rd International Conference on Ultrarelativistic Nucleus-Nucleus Collisions, Quark Matter 2012, August 13-18, 2012, Washington DC

A new lattice action is proposed for the overlap Dirac matrix with nonzero chemical potential. It is shown to preserve the full chiral invariance for all values of lattice spacing exactly. It is further demonstrated to arise in the domain wall formalism by coupling the chemical potential count only to the physically relevant wall modes., Comment: 5 pages, contribution to "Extreme QCD" workshop, 21-23 August 2012, Washington DC, USA

The standard infinite-volume definition of connected correlation function and particle mass in the 3-state Potts model can be implemented in Monte Carlo simulations by using C-periodic spatial boundary conditions. This avoids both the breaking of translation invariance (cold wall b.c.) and the phase-dependent and thus possibly biased evaluation of data (periodic boundary cconditions). The numerical feasibility of the standard definitions is demonstrated by sample computations on a 24*24*48 lattice., Comment: 13 pages + 5 figures Preprint Nos. IC/93/131 and TIFR/TH/93-28

The deconfinement transition in SU(4) lattice gauge theory is studied on N_s^3 X N_t lattices with N_s = 8-16 and N_t = 4-8 using a modified Wilson action which is expected to have no bulk transitions. The peak of susceptibility \chi_{|L|} is found to increase linearly with spatial volume for N_t = 4, 5, and 6, indicating a first order deconfinement phase transition. The latent heat is estimated to be approximately 2/3 of the corresponding ideal gas energy density at T_c., Comment: 3 pages, 2 figures, Lattice2001(hightemp)

We propose a lattice action for the overlap Dirac matrix with nonzero chemical potential which is shown to preserve the chiral invariance on the lattice exactly. We further demonstrate it to arise from the Domain wall by letting the chemical potential count only the physically relevant wall modes., Comment: 4 pages, RevTeX

We compute the quark number susceptibilities in two flavor QCD for staggered fermions by adding the chemical potential as a Lagrange multiplier for the point-split number density term. Since lesser number of quark propagators are required at any order, this method leads to faster computations. We propose a subtraction procedure to remove the inherent undesired lattice terms and check that it works well by comparing our results with the existing ones where the elimination of these terms is analytically guaranteed. We also show that the ratios of susceptibilities are robust, opening a door for better estimates of location of the QCD critical point through the computation of the tenth and twelfth order baryon number susceptibilities without significant additional computational overload., Comment: 10 pages, 12 figures

Screening correlators and masses were studied at finite temperature in QCD with two flavors of dynamical staggered quarks on a lattice. The spectrum of screening masses show a hierarchical approach to chiral symmetry restoration. Control of explicit chiral symmetry breaking through the quark mass was shown to be an important step toward understanding this phenomenon. No sign of decay was found in the finite temperature scalar mesonlike correlators in the confined phase.

The momentum diffusion coefficient for heavy quarks is studied in a deconfined gluon plasma in the static approximation by investigating a correlation function of the color electric field using Monte Carlo techniques. The diffusion coefficient is extracted from the long distance behavior of such a correlator. For temperatures Tc < T, Comment: Minor changes, version to appear in Physical Review D

We study the associated production of $ J/\psi\ + \gamma $ in fixed-target experiments with nuclear targets as well as at the relativistic heavy-ion collider (RHIC). We find that this process affords a very clean probe of $\rho_g$, the ratio of gluon density in a heavy nucleus to that of a proton. The combined $x$ range thus available can be used to discriminate between the predictions of different models of the EMC effect for $\rho_g$., Comment: 10 pages, 4 Figures (not included, available only by p-mail), LaTeX, CERN-TH.6679/92, TIFR/TH/92-59, BU-TH-92/3, Minor revision. Replaced version has the style file equation.sty appended for easy processing, which is the only change

Using both perturbation theory in the Euclidean formalism as well as the non-perturbative Fujikawa's method, we verify that the chiral anomaly equation remains unaffected in continuum QCD in the presence of nonzero chemical potential, \mu. We extend our considerations to lattice fermions with exact chiral symmetry and discuss the consequences for the recent Bloch-Wettig proposal for the Dirac operator at finite chemical potential. We propose a new simpler method of incorporating \mu., Comment: Talk presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, China; 7 pages, 3 figures

I compute the deconfinement order parameter for the SU(2) lattice gauge theory, the Polyakov loop, using the fixed scale approach for two different scales and show how one can obtain a physical, renormalized, order parameter. The generalization to other gauge theories, including quenched or full QCD, is straightforward., Final published version, Added references, Minor Changes, 9pages, 4 Figures

We consider the possibility that color deconfinement and chiral symmetry restoration do not coincide in dense baryonic matter at low temperature. As a consequence, a state of massive "constituent" quarks would exist as an intermediate phase between confined nuclear matter and the plasma of deconfined massless quarks and gluons. We discuss the properties of this state and its relation to the recently proposed quarkyonic matter., 17 pages, 9 figures

We investigate medium effects on mesonic screening lengths for QCD with 2-flavours of dynamical staggered quarks on lattices with cutoff a=1/6T. Denoting the cross-over temperature by $T_c$, we vary the temperature T from 0.89$T_c$ to 1.92$T_c$, spanning both the hadronic and quark gluon plasma phases. While chiral symmetry restoration in the vector channel appears to take place near $T_c$, it is seen in the scalar channel only above 1.33 $T_c$. Varying spatial lattice sizes, we find very little volume dependence in our results at 0.94 $T_c$. We discuss the stability of the scalar meson at these temperatures., Comment: Talk presented at The XXVIII International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Italy

Results of an investigation of the $O(4)$ spin model at finite temperature using anisotropic lattices are presented. In both the large $N$ approximation and numerical simulations using the Wolff cluster algorithm we find that the ratio of the symmetry restoration temperature $T_{\rm SR}$ to the Higgs mass $m_{\rm H}$ is independent of the anisotropy $\xi$. From the numerical simulations we obtain a lower bound of $T_{\rm SR} / m_{\rm H} \simeq 0.58 \pm 0.02$ at a value for the Higgs mass $m_{\rm H}a_s \simeq 0.5$, which is lowered further by about $10\%$ at $m_{\rm H}a_s \simeq 1$. Requiring certain timelike correlation functions to coincide with their spacelike counterparts, quantum and scaling corrections to the anisotropy are determined and are found to be small, i.e., the anisotropy is found to be close to the ratio of spacelike and timelike lattice spacings.

We report results of the investigation of physics at finite chemical potential using the method of Taylor expansion of the free energy for staggered quarks with m π ≃ 210 MeV on N t = 6 lattices. When the spatial volume is (4/T E ) 3 we estimate that the location of the critical end point is at T E /T c ≃ 0.94(1) and μ E B /T E ≃ 1.8(1). This is to be compared to an earlier estimate of T E /T c ≃ 0.95(1) and μ E B /T E ≃ 1.3(3) made on similar spatial volumes and quark masses but with N t = 4.

Studying various thermodynamic quantities for the free domain wall fermions for both finite and infinite fifth dimensional extent N_5, we find that the lattice corrections are minimum for $N_T\geq10$ for both energy density and susceptibility, for its irrelevant parameter M in the range 1.45-1.50. The correction terms are, however, quite large for small lattice sizes of $N_T\leq8$. We propose modifications of the domain wall operator, as well as the overlap operator, to reduce the finite cut-off effects to within 10% of the continuum results of the thermodynamic quantities for the currently used N_T=6-8 lattices. Incorporating chemical potential, we show that \mu^2 divergences are absent for a large class of such domain wall fermion actions although the chiral symmetry is broken for $\mu\neq0$., Comment: 11 pages, 15 figures included

Quantum Chromo Dynamics (QCD), the theory of strong interactions, predicts a transition of the usual matter to a new phase of matter, called Quark-Gluon Plasma (QGP), at sufficiently high temperatures. The non-perturbative technique of defining a theory on a space-time lattice has been used to obtain this and other predictions about the nature of QGP. Heavy ion collisions at the Large Hadron Collider in CERN can potentially test these predictions and thereby test our theoretical understanding of confinement. This brief review aims at providing a glimpse of both these aspects of QGP., Comment: 26 pages, 31 Figures, Invited article for the volume on LHC physics to celebrate the Platinum Jubilee of the Indian National Science Academy, edited by Amitava Datta, Biswarup Mukhopadhyaya and Amitava Raychaudhuri. Needs style file insa.sty (included)

We investigate the Taylor expansion of the baryon number susceptibility, and hence, pressure, in a series in the baryon chemical potential (mu_B) through a lattice simulation with light dynamical staggered quarks at a finer lattice cutoff a=1/6T. We determine the QCD cross over coupling at mu_B=0. We find the radius of convergence of the series at various temeperatures, and bound the location of the QCD critical point to be T^E/T_c = 0.94 and mu_B^E/T < 1.8. We also investigate the extrapolation of various susceptibilities and linkages to finite chemical potential., 16 pages, 12 figures

The thermodynamics of massless ideal gas of overlap quarks has been investigated both analytically and numerically for both zero and nonzero baryon chemical potential. Any \mu^2-divergence is shown analytically to be absent for a class of actions with nonzero chemical potential. All such actions are shown to violate chiral invariance. While the parameter M can be shown to be irrelevant in the continuum limit, as expected, it is shown numerically that the continuum limit can be reached with relatively coarser lattices for certain ranges of M. Numerical limitations of the existing method of introduction of chemical potential are demonstrated. Finally we also show that the energy density for the massive overlap fermions has the correct continuum limit., Comment: 12 Pages, RevTex4, 12 Figures (included), Sections II, III A. reorganised, new Appendix added, more precise results in fig. 3, some new references added, version to be published in Physical Review D

The thermodynamics of massless ideal gas of overlap quarks has been investigated numerically for both zero and nonzero baryon chemical potential $\mu$. While the parameter M has been shown to be irrelevant in the continuum limit, it is shown numerically that the continuum limit can be reached with relatively coarser lattices for certain range of M. Numerical limitation of the existing method of introduction of chemical potential in the overlap formalism is discussed. We have also studied the energy density of free domain wall fermions in the absence of $\mu$ and estimated the extent of lattice in the fifth dimension $L_5$ for which the overlap results are recovered. Interestingly, this value of $L_5$ is also minimum for the same range of M found in the overlap case., Comment: 5 pages, 4 figures, to appear in the proceedings of the 20th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions: Quark Matter 2008 (QM2008)

We present results from high statistics investigations on the 3-d 3-state Potts model with and without antiferromagnetic next-to-nearest neighbour (nnn) couplings. On L3 lattices, with L ranging from 20 to 48, we find a finite size scaling behaviour in all global observables which is characteristic of a first order phase transition in both the cases. Our investigations of the correlation lengths suggest it to be difficult to discern about the order of the phase transition from them alone.

Results from our recent investigations of quark number susceptibilities in both quenched and 2-flavour QCD are presented as a function of valence quark mass and temperature. A strong reduction (~40%) is seen in the strange quark susceptibility above T c in both the cases. A comparison of our isospin susceptibility results with the corresponding weak coupling expansion reveals once again the non-perturbative nature of the plasma up to 3T c . Evidence relating the susceptibility to another non-perturbative phenomena, pionic screening lengths, is presented.

We investigate mesonic screening correlators at T=2T c using the overlap fermions in the quenched approximation, where T c is the QCD phase transition temperature. Using lattices with temporal extent up to 8 we found that both pseudoscalar and vector correlators exhibit a nice cosh behaviour, leading to a plateau behaviour in the local screening masses as a function of distance. The ρ and π masses so determined show very little variation with the lattice spacing a. This augurs well for the use of chiral fermions, and further suggests the small deviations of these masses from the ideal gas values are genuine effects of interactions.

Fluctuations of conserved quantities in heavy-ion collisions have been argued to be diagnostic tools for the nature of the produced phase. These can be related to the predictions of quark number susceptibilities (QNS) from lattice QCD. Using the diagonal QNS, we extracted the Wroblewski parameter in a dynamical QCD computation. Our results on the cross correlations \chi_{BQ}, \chi_{BY}, \chi_{BS} and \chi_{QY} allow us to explore the charge and baryon number of objects that carry flavour. We present evidence that in the high temperature phase of QCD the different flavour quantum numbers are excited in linkages which are exactly the same as one expects from quarks., Comment: 9 pages, 6 Figures, Invited Talk at the International Conference on Strangeness in Quark Matter, ``SQM2006'', UCLA, Los Angeles, USA, Mar. 26-31, 2006